Here the parameters \(a\)  and \(b\)  are conformal weights of \(\rho _l\) , \(\rho _r\) , respectively, and \(\epsilon = d-2\) . The one-dimensional potential \(V_{\rm PT}\)  is known as the Pöschl–Teller potential and the Hamiltonian (REF ) is that of the \(BC_2\)  Calogero–Sutherland system. The derivation of (REF ) along with the computation of the potentials for a number of examples can be found in [1]}, [2]}, [3]}.
